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cheat7.tex
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cheat7.tex
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\documentclass[a4paper,10pt]{article}
\usepackage{mypreamble}
%% Page setup
\geometry{
margin=2cm,
includehead,
includefoot,
headsep=8pt,
footskip=16pt,
}
\pagestyle{fancy}
\MakeSingleHeader% {<l>}{<r>}
{\TextCheatsheetEng: Combinatorics}%
{\TextDiscreteMathEng, \IconSpring~Spring 2022}
\fancyfoot{}
\fancyfoot[L]{\tiny Build time: \DTMnow}
\fancyfoot[R]{\tiny Source code can be found at \url{https://github.com/Lipen/discrete-math-course}}
% \fancyfoot[C]{\thepage\ of \zpageref{LastPage}}
%% Add custom setup below
% \titlespacing{\type}{left}{above}{below}[right]
\titlespacing{\section}{0pt}{*1}{*0.5}
\titlespacing{\subsection}{0pt}{*1}{*0.5}
\declaretheoremstyle[
spaceabove=6pt,
spacebelow=6pt,
postheadspace=0.5em,
notefont=\normalfont\scshape,
]{mystyle}
\declaretheorem[style=mystyle]{theorem}
\tikzset{
dot/.style = {
draw,
fill=black,
shape=circle,
minimum size=4pt,
inner sep=0pt,
outer sep=0pt,
},
circ/.style = {
draw,
% fill=white,
shape=circle,
minimum size=4pt,
inner sep=0pt,
outer sep=0pt,
},
position/.style args={#1:#2 from #3}{
at=(#3.#1), anchor=#1+180, shift=(#1:#2)
},
mylabel/.style args={#1:#2}{
append after command={
(\tikzlastnode.center) node [#1] {#2}
}
},
}
\begin{document}
\selectlanguage{english}
\setcounter{section}{5}
\section{Combinatorics Cheatsheet}
\subsection{Overview}
\begin{terms}
\item \textbf{Combinatorics} is a field of mathematics concerned with:
\begin{terms}
\item Arrangements of elements of a set into patterns satisfying specific rules, generally referred to as \emph{discrete structures}.
\item The existence, enumeration, analysis, classification and optimization of discrete structures.
\item Generalizations and specializations of relations between discrete structures.
\end{terms}
\end{terms}
\subsection{Permutations and Combinations}
\subsubsection{Basic Counting Principles}
\noindent TODO: addition, multiplication, subtraction, bijection, pigeonhole, double counting
\subsubsection{Ordered Arrangements}
\noindent TODO: string, tuple, sequence, map (function), k-permutation, circular permutation
\begin{terms}
\item ...
\end{terms}
\subsubsection{Unordered Arrangements}
\noindent TODO: subset, k-combination, multiset, k-comb of a multiset, k-perm of a multiset, binomial coefficient
\begin{terms}
\item ...
\end{terms}
\subsubsection{Multinomial Coefficients}
\begin{terms}
\item ...
\end{terms}
\subsubsection{The Twelvefold Way%
\texorpdfstring{\hfill\normalsize\href{https://en.wikipedia.org/wiki/Twelvefold_way}{Twelvefold way}}{}}
\begin{terms}
\item ...
\end{terms}
\subsection{Inclusion--Exclusion Principle%
\texorpdfstring{\hfill\normalsize\href{https://en.wikipedia.org/wiki/Inclusion-exclusion_principle}{PIE}}{}}
\noindent TODO: PIE, M\"{o}bius Inversion
% TODO: \subsection{Generating Functions}
% TODO: \subsection{Partitions}
\end{document}